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VECTORS

VECTORS. Section 1 Objectives. The student should be able to: Distinguish between a scalar and a vector Combine vectors using graphical methods Multiply and divide vectors by a scalar. Scalars Need to Know. Specified by a magnitude and a unit 4 m/s 10 kg 10 x 10 12 m.

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VECTORS

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  1. VECTORS

  2. Section 1 Objectives The student should be able to: • Distinguish between a scalar and a vector • Combine vectors using graphical methods • Multiply and divide vectors by a scalar

  3. ScalarsNeed to Know • Specified by a magnitude and a unit • 4 m/s • 10 kg • 10 x 1012 m

  4. VectorNeed to Know • Specified by a magnitude and unit AND DIRECTION • 4 m/s heading west • 10 x 1012 m north • 10 m/s2 down • As long as the direction and magnitude are kept the same you can move the vector anywhere

  5. Vector RepresentationNeed to Know • On a drawing, a vector is represented by an arrow • The length of the vector is proportional to the magnitude • In print, a vector is usually bold • In hand written work, a vector can be indicated by an arrow over it

  6. Vector AdditionNeed to Know • If they are collinear, simple arithmetic can be used • Simple arithmetic can not be used if they are not collinear • The sum of a given set of vectors is called the resultant

  7. Example Suppose you drive 200 km to the east and then 50 km to the west. What is your totaldisplacement? 200 km east (+) 150 km east (+) 50 km west (-) Since they are parallel I can add arithmetically I assume everything going to the right is positive And everything going to the left is negative Displacement = 200 km – 50 km Resultant = 150 km to east (+)

  8. What if they are not collinear or parallel? • We can add them together graphically • Tip to tail method • Parallelogram method • We can add them together mathematically with trigonometry (oh my!)

  9. Graphical AdditionNeed to Know • Tip to Tail method: • Draw first vector to scale • Draw second vector to scale, placing its tail at the first vector’s tip (make sure your directions are correct!) • Draw an arrow from the tail of the first vector to the tip of the second vector. This is the resultant of the two vectors • Approximate the length of the resultant

  10. Tip to Tail Method 15 m + 20 m Tips Line up Resultant Approximately ≈ 25 m 15 m Tails Line up Tip to tail 20 m

  11. Tip to Tail Method + 10 m 20 m Resultant ≈ 25 m 10 m 20 m

  12. Website Example Adding vectors tip to tail Simulation Tip to tail with numbers

  13. 10 = + 10 Resultant

  14. + 10 12 = 10 +

  15. Multiplying Vectors by Scalars A vector can be multiplied (or divided) by a scalar Result is a vector 5

  16. Graphical AdditionNeed to Know • Parallelogram method • The tails of the vectors are drawn from a common origin • Parallelogram is constructed using these two vectors as adjacent sides • The resultant is drawn from the common origin • We can only add two at a time with this method

  17. Parallelogram Method 20 m + 15 m Create parallelogram with opposite sides ≈ 23 m 15 m Tails are together 20 m

  18. Parallelogram Method 15 + 30 15 ≈35 30

  19. = +

  20. = +

  21. Graphical Addition Bottom Line: Gives a good approximate direction and magnitude of the resultant vector. For the most accurate results you must add your vectors mathematically!! That is next ….. but first what do you recall about vectors

  22. :25 94 m/s is a • Vector • Scalar • Direction Correct answer is 2—scalar

  23. :14 94 m/s going west is a • Vector • Scalar • Direction Correct answer is 1--vector

  24. :00 A vector has • Direction and magnitude • Magnitude only • Direction only Correct Answer is 1

  25. 0 Seconds Remaining The drawing indicates what type of vector addition? • Tip to tail • Parallelogram Correct Answer is 2

  26. 0 Seconds Remaining The drawing indicates what type of vector addition? • Tip to tail • Parallelogram Correct Answer is 1

  27. Properties of Vectors • Vectors can be moved parallel to themselves in a diagram • Vectors can be added in any order • To subtract a vector, add its opposite

  28. Practice • Quest Vectors assignment

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